ORDER OF OPERATIONS How to do a math problem with more than one operation in the correct order.

Objective I will be able to apply the order of operations to simplify expressions. I will be able to apply the order of operations to simplify expressions.

VOCABULARY Numerical Expression A collection of numbers, operations, and grouping symbols Grouping Symbols Characters used to change the order of operations in an expression EX: ( ) Parenthesis [ ] Brackets Division Bar ----

VOCABULARY Order of operations A procedure for evaluating an expression involving more than one operation PEMDAS ( ) 3² x/÷ (WHICHEVER COMES 1 ST ) +/- (WHICHEVER COMES 1 ST )

Simplify To simplify an expression when there are more than two operations in the expression, you must use a set of rules called the order of operations. To simplify an expression when there are more than two operations in the expression, you must use a set of rules called the order of operations.

ORDER OF OPERATIONS 1. Simplify the terms within parentheses. 2. Simplify the terms with exponents. 3. Multiply and divide from left to right. 4. Add and subtract from left to right. PEMDAS

PEMDAS Remember the order by the phrase Remember the order by the phrase Please Please Excuse Excuse My Dear My Dear Aunt Sally Aunt Sally

The “P” and “E” The “P” stands for items in parenthesis The “P” stands for items in parenthesis Do all items in the parenthesis first Do all items in the parenthesis first The “E” stands for Exponents Do anything that has a exponent (power) 8282

The “MD” Represents Multiply and Divide Represents Multiply and Divide Do which ever one of these comes first in the problem Do which ever one of these comes first in the problem Work these two operations from left to right

The “AS” Represents Add and Subtract Represents Add and Subtract Do which ever one of these comes first Do which ever one of these comes first Work left to right Work left to right

Example Find 8 + (4 x 24) ÷ 32 Find 8 + (4 x 24) ÷ 32 Step 1: Simplify within the parentheses. 8 + (4 x 24) ÷ (96) ÷ 32 Step 2: Divide 96 ÷ Step 3: Add Solution: 8 + (4 x 24) ÷ 32 = X

What happens if we don’t follow the order of operations? If we just work the problem from left to right, we won’t get the correct answer! If we just work the problem from left to right, we won’t get the correct answer! 8 + (4 x 24) ÷ = x24 = ÷ does not equal 11!

Another Example Simplify: (20 – 2) ÷ 3 Step 1: Simplify within parentheses (20 -2) ÷ 3 Step 2: Divide (18) ÷ 3 Solution: (20 – 2) ÷ 3 = 6

Look at the two students and decide which one correctly followed the order of operations! Janet 14 – (5+2) X 2 14 – 7 x 2 7 x 2 14 John 14 – (5+2) X 2 14 – 7 x 2 14 – 14 0

PEMDAS (9+1)

PEMDAS 3 (9+1) (10)+6 2 3(10)

Let’s practice! You have 5 seconds : take out your whiteboard, expo marker, and felt eraser.

PEMDAS 4+5 x (6-2) 4+5 x

PEMDAS x x

PEMDAS  

PEMDAS x –2 x

PEMDAS 64  (9 x 3-19) 64  (27 –19) 64  8 8

PROPERTIES COMMUTATIVE (+) = a + b = b + a COMMUTATIVE (+) = a + b = b + a COMMUTATIVE (x) 4 x 9 = 9 x 4 ab = ba COMMUTATIVE (x) 4 x 9 = 9 x 4 ab = ba ASSOCIATIVE (+) 3 + (5+1) = (3+5) + 1 ASSOCIATIVE (+) 3 + (5+1) = (3+5) + 1 a + (b+c) = (a+b) + c a + (b+c) = (a+b) + c  ASSOCIATIVE (x) 8 x (2x9) = (8x2) x 9 a(bc) = (ab)c  DISTRIBUTIVE

1) 5 + (12 – 3) ) 8 – ) 39 ÷ (9 + 4) 39 ÷ ÷ 13 3 YOUR TURN … ON SLATES!!! YOU HAVE 5 SECONDS!!!

4) ÷ 2 – ) , ,000 15,000 15,000 6) 36 ÷ (1 + 2) 2 36 ÷ ÷ ÷ 9 36 ÷ 9 4 7) , ,000 30,000 30,000

8) (5 – 1) 3 ÷ ÷ ÷ 4 64 ÷ 4 64 ÷ ) (7 -2) – – – – –